🔵 Sphere Calculator 2026
Calculate surface area, volume, radius, diameter, and circumference
Enter Radius
r = radius, d = diameter
📊 Results
Radius (r)
5 cm
Diameter (d)
10 cm
Circumference
31.42 cm
Surface Area
314.16 cm²
Volume
523.6 cm³
A/V Ratio
0.6 /cm
📝 Step-by-Step Solution
Given: r = 5 cm → d = 2r = 10 cm
Circumference = 2πr = 2π × 5 = 31.42 cm
Surface Area = 4πr² = 4π × 25 = 314.16 cm²
Volume = (4/3)πr³ = (4/3)π × 125 = 523.60 cm³
📐 Sphere Formulas
Diameter: d = 2r
Circumference: C = 2πr = πd
Surface Area: A = 4πr²
Volume: V = (4/3)πr³
Radius from Area: r = √(A / 4π)
Radius from Volume: r = ∛(3V / 4π)
Understanding Sphere Geometry
🔵 What is a Sphere?
All points equidistant from center. Perfectly round 3D shape. No edges, no vertices. The most efficient shape (minimizes surface for given volume).
📐 Surface Area
A = 4πr². Exactly 4 times the area of a great circle. All surface points equidistant from center. Used for paint, coatings.
📦 Volume
V = (4/3)πr³. Space inside sphere. Ball ≈ 52% of smallest enclosing cube. Maximizes volume for given surface.
⭕ Great Circle
Largest circle on sphere surface. Radius = sphere radius. Divides sphere in half. Circumference = 2πr.
Frequently Asked Questions
What is the surface area formula for a sphere?
A = 4πr². Four times pi times radius squared. Can also write as
πd² using diameter. Example: r=5 → A = 4π×25 = 314.16
What is the volume formula for a sphere?
V = (4/3)πr³. Four-thirds pi times radius cubed. Example: r=5 → V
= (4/3)π×125 = 523.6 cubic units.
How do I find radius from surface area?
r = √(A / 4π). Divide area by 4π, then square root. Example:
A=314.16 → r = √(314.16/12.57) = 5.
How do I find radius from volume?
r = ∛(3V / 4π). Cube root of (3V divided by 4π). Example: V=523.6
→ r = ∛(1570.8/12.57) = 5.
What is the circumference of a sphere?
C = 2πr = πd. The great circle circumference. Same as a circle
with plane through center.
What is the relationship between diameter and radius?
d = 2r. Diameter goes all the way through center. Radius is half
the diameter.
How does doubling the radius affect volume?
Volume increases 8×. V ∝ r³, so (2r)³ = 8r³. Surface area
increases 4× (2r)² = 4r².
What is surface area to volume ratio?
A/V = 3/r. Decreases as sphere grows. Important in biology,
physics. Small things have relatively more surface.
Why is sphere the most efficient shape?
Minimizes surface area for given volume. Soap bubbles, planets,
water drops all tend toward spherical. Isoperimetric inequality.
What are real-world examples of spheres?
Balls, planets, oranges, bubbles, marbles, beads, globes, ball
bearings. Many things approximate spheres.
What is a great circle?
Cross-section through center. Largest possible circle on sphere.
Earth's equator is great circle. Shortest path on sphere follows great circles.
How do I find area of hemisphere?
Curved surface: 2πr². Total (including flat circle): 2πr² + πr² =
3πr². Half of sphere surface is 2πr².
What is the difference between sphere and ball?
Sphere: surface only (hollow). Ball: solid
(filled interior). Mathematically different. In common use, often synonyms.
How do I calculate paint for a sphere?
Use surface area: 4πr². Divide by paint coverage (sq ft/gallon).
Add for multiple coats, texture, waste.
What is the volume of Earth?
≈ 1.08 × 10¹² km³. Earth radius ≈ 6,371 km. V = (4/3)π × 6371³.
Earth is slightly oblate (bulges at equator).
How do I find volume from circumference?
First find radius: r = C/2π. Then V = (4/3)πr³. Or directly: V =
C³/(6π²).
How accurate is this calculator?
Uses precise mathematical formulas with π to full precision.
Results are exact for perfect spheres.